Page History

Extended Range - CDFs and EFIs

ecChart display.

To complement the EFI and SOT for two parameters in the extended range (introduced with IFS cycle 46r1 in June 2019) a facility to view extended-range Cumulative Distribution Functions (CDFs) for those parameters was also introduced (in February 2020).  Unlike ECMWF's pre-existing CDF-viewing tools, used for 24h periods at shorter ranges, which show absolute values, these CDFs depict anomalies (relative to the ER-M-Climate distribution).  They cover the following:

Parameters:

7-day mean 2m temperature anomaly
7-day total precipitation anomaly.

Forecast time steps: 

000-168h, 096-264h, 168-336h, 264-432h, 336-504h, 432-600h, 504-672h, 600-768h, 672-840h, 768-936h, 840-1008h, 936-1104h 

...

Fig8.2.6.2: The EFI and SOT for 2-metre weekly mean temperature anomalies, and CDF plots of temperature and precipitation anomalies for one site (see green pin). On the CDF widget the black curve represents the ERM-climate and coloured curves represent the different extended-range forecasts valid for the same 7-day period.

Consideration when interpreting the charts

At these longer forecast times in the extended range the latest run may not necessarily be the best and users may wish to consider more than one set of solutions as a lagged ensemble.  In the example shown in Fig8.2.6.2 the latest forecast temperature anomaly CDF (in red) shows a strong positive anomaly while previous forecasts suggested a more modest warm signal.

Plot design.

For both precipitation and temperature, zero on the x-axis (and the thicker vertical gridline) simply corresponds to ERM-climate mean values (for the location, the time of year and the lead time displayed), because of course "anomaly" computations use these mean values as their reference points. This statement is true for all of the curves. However, for different lead times (i.e. the different coloured curves) the absolute value that is the mean will vary a little bit (due to model drift and under-sampling). In spite of such variations it is still reasonable, helpful and recommended to inter-compare the single black ERM-climate curve with all the coloured curves (even if this is only strictly valid for the same lead time that it represents - i.e. the red curve).

...

For temperature, the x-axis starts from the overall minimum encountered within all the displayed CDFs (ERM-climate and ensemble forecasts).

An example.

Extended range charts for EFI and SOT are available on ecCharts.  These are:

...

Note that whilst negative SOT values can be computed, and are displayed in meteogram format (as above), and are illustrated below, we advise the user to generally focus on SOT values that are ≥0.8.

Extended Range CDFs.

Cumulative Distribution Function (CDF)s for ensemble temperature and rainfall forecasts may be constructed from ensemble extended range forecasts.   It is important to note that here it is anomalies from the "norm" that are considered rather than absolute temperature or rainfall values.  The anomalies for the extended range climate (ER-M-climate) (black line) are the frequencies of departures from the mean (here defined as the "norm") of the ER-M-climate for the date in question (i.e.the light green lines on the diagram indicate the value at 50% probability and marked as 0°C anomaly).   Some anomalies are positive, some in the tails of the plot are extremely positive; some are negative, some some in the tails of the plot extremely negative.   The CDF for the ensemble values is constructed from the anomaly of the temperature forecast by each ensemble member (red line) as a departure from the mean or "norm" of the ER-M-climate.

Extreme Forecast Index (EFI) and Shift of Tails (SOT) are derived in the same way as for the medium range products.

Examples of CDF and derivation of SOT

Example of Temperature CDFs: Upper tail positive SOT

Fig8.2.6.6A: The large positive EFI shows the ensemble temperature anomaly distribution is for warmer anomalies much above the ER-M-climate anomaly distribution.  The positive upper tail SOT (quantile 90) indicates there are several ensemble members predicting extreme warm temperature anomalies (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests a warm temperature anomaly may be confidently forecast (large positive EFI), probably exceptional but not necessarily extreme (SOT +0.4).  Confidence in extreme temperatures rises as SOT values increase - users should focus on SOT values >0.5.

Example of Temperature CDFs: Upper tail positive SOT

Fig8.2.6.6B: The large positive EFI shows the ensemble temperature anomaly distribution is for warmer anomalies much above the ER-M-climate anomaly distribution.  The negative upper tail SOT (quantile 90) indicates generally ensemble members are not predicting an extreme temperature anomaly (above the 99th ER-M-climate percentile shown by the dashed green line) - however, note one ensemble member (extreme top end of red curve) is predicting an extreme temperature anomaly (above the 99th ER-M-climate percentile) though less extreme than the extreme of ER-M-climate anomaly.   This suggests a warm temperature anomaly is confidently forecast (fairly large positive EFI), but will be unexceptional (SOT –0.7) compared with ER-M-climate - but nevertheless one member does suggest a near exceptional warm anomaly is possible.

Example of Temperature CDFs: Lower tail negative SOT

Fig8.2.6.6C: The small positive EFI suggests the frequencies of ensemble temperature anomaly distribution is near or a little above the ER-M-climate anomaly distribution.  The negative lower tail SOT (quantile 10) indicates generally ensemble members are not predicting an extreme temperature anomaly (below the 1st ER-M-climate percentile shown by the dashed green line) - however note one ensemble member (extreme bottom end of red curve) is predicting an extreme temperature anomaly (below the 1st M-climate percentile) though less extreme than the ER-M-climate anomaly.   This suggests the temperature anomalies are similar to the ER-M-climate anomaly distribution (small positive/negative EFI), and a cold anomaly, if it occurs, will  be unexceptional compared with ER-M-climate (SOT –1.7) - but nevertheless one member does suggest an exceptional cold anomaly is possible.

A similar CDF diagram would be obtained at Nizhniy Novgorod in Fig8.2.6.5B above.

Example of Temperature CDFs: Lower tail negative SOT

Fig8.2.6.6D: The large negative EFI shows the frequencies of ensemble temperature anomaly distribution is for colder anomalies well below the ER-M-climate anomaly distribution.  The positive lower tail SOT (quantile 10)  indicates there are several ensemble members predicting extreme cold temperature anomalies (below the 1st ER-M-climate percentile shown by the dashed green line).   This suggests a cold temperature anomaly may be confidently forecast (large negative EFI), exceptional and probably extreme (SOT +0.95).  Confidence in extreme temperatures rises as SOT values increase - users should focus on SOT values >0.5.

A similar CDF diagram would be obtained at Nizhniy Novgorod in Fig8.2.6.5A above.

Examples of Rainfall CDFs

It should be remembered that only upper tail SOT may be derived from rainfall CDFs as clearly there are no rainfall totals below 0mm and no anomaly in the extended range model climatology can exist below this value.

Example of Rainfall CDF: positive SOT 

Fig8.2.6.7A: An example CDF for snowfall - snowfall is just considered as equivalent rainfall.   Moderately large positive EFI shows the equivalent rainfall anomaly distribution is above the ER-M-climate anomaly distribution.  The positive upper tail SOT (quantile 90) indicates there are several ensemble members predicting extreme equivalent rainfall anomalies (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests uncertainty that a significant equivalent rainfall anomaly is forecast (moderate EFI.  Note: 50% of ensemble members forecast less than about 1mm precipitation (the lower part of the ER-M-climate only just above 0mm), but equally 25% of ensemble members forecast more than about 2mm precipitation (significantly above ER-M-climate where about 97% of precipitation less than 2mm). If a significant rainfall occurs it could be an exceptional rainfall equivalent (SOT 0.8).  Confidence in extreme rainfall rises as SOT values increase - users should focus on SOT values >0.5.

Example of Rainfall CDF: negative SOT  

Fig8.2.6.7B: The moderate positive EFI suggests the ensemble rainfall anomaly distribution is slightly above the ERM-climate anomaly distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members predicting extreme equivalent rainfall anomalies (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests uncertainty that larger than normal rainfall anomaly may be forecast (moderate EFI - but note 70% of ensemble members forecast less than about 1mm precipitation, equally 15% of ensemble members forecast more than about 2mm precipitation), but it is unlikely there will be an exceptional rainfall event (SOT -0.6).

Example of Rainfall CDF: negative SOT 

Fig8.2.6.7C: An example of a rainfall CDF most frequently encountered where very few ensemble members forecast any rain at all.  The small negative EFI shows the ensemble rainfall anomaly distribution is lower than the ER-M-climate anomaly distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members (and in this case none of them) predict extreme equivalent rainfall anomalies (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests confidence that larger than normal rainfall anomaly will not occur (small EFI) and an exceptional rainfall event will not occur(SOT -1.2).

Reliability diagrams in Extended Range.

Reliability diagrams are available for extended range forecasts. This gives an assessment of the current model characteristics and allows some indication of the confidence one can have in the evolution shown within the extended ranges - unless there is good evidence to the contrary (e.g. a major change from previous forecasts in the evolution within the medium range).

...